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At a factory that produces pistons for cars, Machine 1 produced 413 satisfactory pistons and 177 unsatisfactory pistons today. Machine 2 produced 350 satisfactory pistons and 150 unsatisfactory pistons today. Suppose that one piston from Machine 1 and one piston from Machine 2 are chosen at random from today's batch. What is the probability that the piston chosen from Machine 1 is unsatisfactory and the piston chosen from Machine 2 is satisfactory ?